I was reading a bit about characteristic classes when I came across the following theorem:
If a manifold of dimension $4n$ can be embedded as a hypersurface in $\Bbb R^{4n+1}$, then all it's pontryagin numbers vanish
I was looking for an example of a manifold of dimension $4n$, which cannot be embedded in $\Bbb R^{4n+1}$. That is, I'm looking for a $4n$-manifold which has non-zero pontryagin numbers. Since I'm new to this concept, I've no idea how to proceed. Is there a natural example of such a manifold?